Dec 2015
Master of Business Administration (MBA) Examination
I Semester
Mathematics and Statistics for Managers
Time : 3 Hours] [ Max. Marks : 80

Note : Attempt any five. questions with a minimum of two questions from each section. All questions carry equal marks.
Section A
1. (a) Examine the continuity of the function :
                                f(x)= |x| + |x-1| + |x-2| at x = 2.
(b) Evaluate :

2.(a) Find the largest and the smallest value of the polynomial x3 –18x2 +96x in the interval [0, 9].
(b) Evaluates Tg approximately by the use of differential.

3.(a) The marginal cost of production of a firm is given by:

C' (x) = (d/dx) C(x) = 5 + 0.13x
The marginal revenue is given as (d/dx) R(x) = R' (x) = 18. The fixed cost is Rs. 120. Calculate the total (maximum) profit.
(ba) A man borrowed Rs. 20,000 at 6% compound interest promising to repay Rs, 5,000 at the end of each of the first 4 years to reduce principal and interest and to pay the balance at the end of 5th year. Find the amount of his final payment.
4. (a) Find the inverse of the matrix :
            1 –1 0
            2 3 4
            0 1 2
(b) Find the values of a, b and c if the matrix A is given by :
                   a 2 2
A=(1/3)       2 1 b
                   2 c 1
and further it obeys the law AA' – I, where A denotes the transpose of A and I is the unit matrix of order 3.
  Section B

5. (a) The chances that doctor A will diagnose a disease X correctly is
60%. The chances that a patient will die by his treatment alter the correct diagnosis is 40% and the chances of death by wrong diagnosis is 70%. A patient of doctor A, who had disease X died. What is the probability that his disease was diagnosed correctly ?
(b) Write a note on Normal Distribution and discuss its characteristics.

6. (a) The Spearman's Rank Correlation between the marks obtained by 10 students in two Subjects A and B was found to be 0.5. It was later found that the difference in ranks in the above two subjects obtained by one of the students was wrongly taken as 3 instead of the correct difference 7. Find the correct value of the rank-correlation.
(b) What do you mean by Regression? Why there are only two regression lines ? Discuss the properties of the regression coefficients.

7. (a) Write a explanatory note on different models used in Time Series and discuss its different components.
(b) Fit a straight line trend by the method of least squares to the following data. Assuming; that the same rate of change continues, what would be the predicted earnings for the year 1985 ?
Year :                 1976     1977     1978     1979         1980     1981     1982     1983
Sales (Lakh Rs.) : 76     80         130         144         138         120         174        190


8. (a) Discuss the Essential elements of decision-making problem.
(b) What is decision under risk? Discuss the steps to obtain expected Monetary Value (EMV) and state its significance.